Drop rate
The drop rate is the frequency at which a monster is expected to yield a certain item when killed by players. When calculating a drop rate, divide the number of times you have gotten the certain item, by the total number of that monster that you have killed. For example: *Bones have a 100% drop rate from chickens. *Feathers have approximately a 75% drop rate from chickens. Drop rate All items have a chance of being dropped that is expressible as a number—their drop rate. Drop rates are not necessarily a guarantee. An item, for example, with a drop rate of "1 in 5" does not equate to: "This item will be dropped after five kills." While each kill does nothing to increase the drop rate itself, it is trivial to state that more kills gives rise to more chance overall. A popular misconception is that you are guaranteed that item when you kill the monster n number of times, where \frac{1}{n} is the drop rate, or that the likelihood increases with every kill (also known as ). You are never guaranteed anything, no matter how many of that monster you kill; the probability will infinitely approach 1 (100%) with each roll on the drop table. For example: If the King Black Dragon is expected to drop a draconic visage once out of 5,000 kills, then the probability of getting a drop from one kill is as follows: : \begin{align} & 1-\left(1-\frac{1}{5000}\right)^{1} \\ = & \ 1-\left(\frac{4999}{5000}\right)^{1}\\ = & \ 1 - 0.9998 \\ = & \ 0.0002 \\ \end{align} That is 0.02%. To find the drop chance in 5,000 kills, we can raise the equation inside the parenthesis to the 5,000th power, which yields a meagre 63.2% chance of getting a visage, i.e. 1-\left(\frac{4999}{5000}\right)^{5000} \approx 0.632 . Similarly, we can solve for the number of KBDs you need to kill to have a 90% probability of getting one when you kill them: : \begin{align} & \ 1-\left(\frac{4999}{5000}\right)^{x} = 0.90 \\ & x = \frac{ln(1-0.9)}{ln(\frac{4999}{5000})} \\ & x \approx 11511.774 \approx 11512 \\ \end{align} This yields the answer 11,512 meaning that you need to kill 11,512 for a 90% chance of getting a visage. Extra information Again, using the King Black Dragon expected to drop a draconic visage once out of 5,000 kills, the probability of getting said drop twice from two kills or back-to-back is as follows: : \begin{align} & 1-\left1-\left(\frac{1}{5000}\right)^{2}\right \\ = & \ 1-\left(\frac{24999999}{25000000}\right)\\ = & \ 1 - 0.99999996 \\ = & \ 0.00000004 = 0.000004%\\ \end{align} Binomial model Given a known value of \frac{1}{x} , the chance of receiving such an item k times in n kills can be calculated using . The probability of receiving an item k times in n kills with a drop rate of \frac{1}{x} = p follows: : \binom n k p^k(1-p)^{n-k} , where \binom n k =\frac{n!}{k!(n-k)!} For finding the probability of obtaining an item at least once, rather than a specified number of times, we can drop the binomial coefficient and simply the equation to: : 1 - (1 - p)^x , where (1-p)^x is calculating the probability of not receiving the item, and we use that to calculate the inverse. For example, it is known that the drop rate of the draconic visage is \frac{1}{10000} = 0.0001 . If we want to know the probability of receiving one visage in a task of 234 Skeletal Wyverns, we would plug into the equation: : \begin{align} & 1 - (1 - 0.0001)^{234} \\ = & \ 1 - 0.9999^{234} \\ \approx & \ 1 - 0.97687 \\ \approx & \ 0.023129 \end{align} Giving us the answer, we have approximately a 2.3% chance of receiving a visage during this task. Random number generator The random-number generator (or RNG) functions similarly to drop rates. It generates an unpredictable, random sequence of numbers, thus denoting a random chance. For example, if you kill a lizardman shaman, there's a 1 in 5,000 chance it drops a dragon warhammer, so a function object, such as a die, has a 1 in 5,000 chance of rolling on 5,000 each kill, which would result in receiving the drop. See also *Drops *Rare drop table *Items *Kill count *Bestiary *Player identification number Category:Mechanics